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A182154
Smallest k >= 2 such that k^(2^n)+1 is the lesser member of a twin prime pair.
1
2, 2, 2, 4, 2, 49592, 7132, 532, 333482, 2226686, 3543554, 23379038, 1249625230, 188489906
OFFSET
0,1
COMMENTS
These lesser of twin prime pairs are also generalized Fermat primes, (not possible for greater of twin prime pairs, except for 5).
When extending this sequence, it is useful if the primes b^(2^n)+1 are known in advance (Gallot link). - Jeppe Stig Nielsen, Sep 25 2019
For later terms, the bigger twin is only a probable prime, not a proven prime. - Jeppe Stig Nielsen, Nov 24 2022
LINKS
PrimeGrid and "Stream", GFN-1x Small Primes search, mentions a(12) and a(13).
EXAMPLE
2^(2^4)+1 = 65537 = A001359(861), then a(4) = 2.
MATHEMATICA
Table[k=2; While[!PrimeQ[k^(2^n)+1]||!PrimeQ[k^(2^n +3], k++]; k, {n, 0, 7}]
CROSSREFS
Sequence in context: A366628 A320305 A064025 * A273875 A054709 A121806
KEYWORD
nonn,more,hard
AUTHOR
Manuel Valdivia, Apr 15 2012
EXTENSIONS
a(8)-a(10) from Jeppe Stig Nielsen, Sep 25 2019
Name edited by Felix Fröhlich, Sep 25 2019
a(11)-a(13) from Jeppe Stig Nielsen, Nov 24 2022
STATUS
approved